Understanding the Problem

Compound interest is a financial concept used to calculate the interest earned on a principal amount over multiple compounding periods. The formula to calculate compound interest is:

Compound Interest (CI) = Principal Amount * [(1 + (Rate of Interest / 100)) ** Time] – Principal Amount

In this tutorial, we’ll develop a Python program to calculate compound interest by taking user inputs for the principal amount, rate of interest, time, and compounding frequency.

Developing the Algorithm

-> Take user input for the principal amount, rate of interest, time period, and compounding frequency.

-> Calculate the compound interest using the provided formula.

-> Display the calculated compound interest to the user.

Writing the Python Code

# Function to calculate compound interest
def calculate_compound_interest(principal, rate, time, frequency):
    amount = principal * (1 + (rate / (100 * frequency))) ** (frequency * time)
    compound_interest = amount - principal
    return compound_interest

# Main function
def main():
    # Input principal amount, rate of interest, time period, and compounding frequency
    principal_amount = float(input("Enter the principal amount: "))
    rate_of_interest = float(input("Enter the rate of interest: "))
    time_period = float(input("Enter the time period (in years): "))
    compounding_frequency = int(input("Enter the compounding frequency per year: "))

    # Calculate compound interest
    compound_interest = calculate_compound_interest(principal_amount, rate_of_interest, time_period, compounding_frequency)

    # Display the result
    print("Compound Interest:", compound_interest)

if __name__ == "__main__":
    main()

O/P

Enter the principal amount: 5000
Enter the rate of interest: 5.5
Enter the time period (in years): 2
Enter the compounding frequency per year: 12
Compound Interest: 579.99

Time Complexity

The time complexity of this program is constant (O(1)) because the execution time is not dependent on the input values. The program will always execute a fixed number of operations regardless of the values entered by the user.

Code Explanation

We define a function calculate_compound_interest that takes four arguments: principal, rate, time, and frequency. Inside the function, we calculate the compound interest using the provided formula and return the result.

The main function is defined to take user input for the principal amount, rate of interest, time period, and compounding frequency.

User inputs are converted to floating-point numbers using float(input(…)) and an integer using int(input(…)).

The calculate_compound_interest function is called with the user-provided inputs, and the result is stored in the compound_interest variable.

Finally, the calculated compound interest is displayed to the user.

Dry Run

Let’s perform a dry run of the program with the following inputs:

Principal amount = 5000
Rate of interest = 5.5
Time period = 2
Compounding frequency = 12 (monthly compounding)

Execution:

User enters the principal amount: 5000
User enters the rate of interest: 5.5
User enters the time period (in years): 2
User enters the compounding frequency per year: 12

The calculate_compound_interest function is called with principal_amount = 5000, rate_of_interest = 5.5, time_period = 2, and compounding_frequency = 12.

The compound interest is calculated as follows:

amount = 5000 * (1 + (5.5 / (100 * 12))) ** (12 * 2) ≈ 5579.9775216
compound_interest = 5579.9775216 - 5000 ≈ 579.99 (after rounding)

The calculated compound interest (approximately 579.99) is displayed to the user.

The program successfully calculates and displays the compound interest based on the user inputs.